3. resistance of a ship - ulisboa · pdf file9 3. resistance of a ship 3.2 estimates based on...

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• In the preliminary stages of ship design, the resistance

coefficient is estimated with approximate methods based

on systematic series or statistical regressions to

experimental data.

• A systematic series is a family of ship hulls obtained from

a systematic variation of one or more shape parameters.

Usually, the changes are based on a parent form. The

resistance of all the models that constitute a series is

measured experimentally. This database allows the

interpolation of the resistance coefficient for other shapes

originated by parametric variations of the original shape

3. Resistance of a Ship3.2 Estimates based on statistical methods

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• The Froude number is related to the fineness coefficient.

Ships with a high Froude number exhibit a resistance

coefficient dominated by the wave resistance and have a

smaller fineness coefficient.

• The longitudinal distribution of the displacement affects

the resistance and is related to the Froude number. This

distribution is caracterized by the buoyancy centre. For

ships with low Froude number, the resistance is dominated

by the flow separation region that might occur at the stern.

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• The risk of flow separation is reduced if the buoyancy

centre is upstream of midship. In the case of high Froude

numbers, wave resistance dominates the resistance

coefficient. In these cases, the crictical region is the bow,

which should be thinner moving the buoyancy centre to a

location downstream of midship.

• The vertical displacement is influenced by the choice of V

or U sections. U shaped sections lead to smaller wave

resistance than V shapes, but to highest risk of flow

separation.

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Taylor series

• Taylor performed model tests (between 1907 and 1914) for

systematic variations of a parent form defined by the

British cruiser “Leviathan”.

• Systematic variations of models shape:

– 5 ratios length/displacement1/3:

– 3 ratios beam/draft: 2,25, 2,92 e 3,75

– 8 prismatic coefficients: from 0,48 a 0,86

– Only 2 values of B/T 2,25 and 3,75 were used by

Taylor: 80 models.

3/1/ ∆L

TB /

pC

)/,,/,/(3

wlpwlR LCTBLVfC ∆=

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Taylor series

• Reanalysis of the results by Gertler (1954).

– Corrections for water temperature, laminar flow and

blockage.

– Viscous resistance from Schoenherr line. Froude’s

method. Results give residual resistance.

– B/T=2,92 was converted to 3.

– 117 diagrams of residual resistance.

)/,,/,/(3

wlpwlR LCTBLVfC ∆=

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Taylor series

• Taylor’s parent form.

• Fineness coefficient of main section 0,925.

• Hull centre at midship.

• Stern for two propellers.

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Taylor series

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Other series

• Série 60 (Todd, 1960)

– Single screw merchant ship

– 5 parent forms with fineness coefficients: 0,60, 0,65,

0,70, 0,75 and 0,80.

– For each fineness coefficient, the location of the hull

centre was optimized.

– Variations of L/B, B/T, etc.

• Other series include BSRA, SSPA, NPL,...

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Method of Holtrop and Mennen

• The method estimates the resistance of displacement ships.

• Statistical regression of model tests and results from ship trials.

• The database covers a wide range of ships. For extreme shapes the number of cases in the database is small. Therefore, the accuracy of the estimates is worse.

• The method may be used to assess qualitatively the resistance of a ship design.

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• Two formulations:

– Standard method – Method of Holtrop and Mennen: J. Holtrop, “A statistical re-analysis of resistance and propulsion data”, ISP, Vol. 31, No. 363, November 1984.

– “Improved” method: J. Holtrop, “A statistical resistance prediction method with a speed dependent form factor”, SMSSH’88, Varna, Oct. 1988.

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3.2 Previsão da resistência do navio com métodos estatísticos

Método de Holtrop e Mennen

• Resistance decomposition:

� = Total resistance

� = Friction resistance from the ITTC 1957 line

� = Form factor of bare hull

� = Wave resistance of bare hull

� = Wave resistance of the bulbous bow

AAPPTRBwFT RRRRRRkR ++++++= )1( 1

TR

FR

11 k+

wR

BR



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• Resistance decomposition:

� = Additional resistance from the immersed

Transom

� = Appendage resistance

� = Correlation allowance

.

AAPPTRBwFT RRRRRRkR ++++++= )1( 1

TRR

APPR

AR



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• Form factor of bare hull:

• Wave resistance:

� = Displacement

� = Fineness coefficient

� L = Length at fluctuation

� B = Beam

� T = Draft

� LCB = Longitudinal position of hull centre

),,,/,/,/,/,/,,( 3pbfTBTMn

w ChTBTABTATBBLLCFfg

R∇=

∇ρ

∇

MC

),/,,/,/(1 31 pCLLCBTLBLfk ∇=+




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• Wave resistance:

� = Prismatic coefficient

� = Tranversal section of transom at rest

� = Transversal section of bulbous bow

� = Vertical distance from the bulbous section

centre to the keel line (m)

� = Draft at the bow (m)

� = Froude number

),,,/,/,/,/,/,,( 3pbfTBTMn

w ChTBTABTATBBLLCFfg

R∇=

∇ρ


pC

TA

BTA

bh

fT

nF



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• Regression formula for the wetted surface

– Fineness coefficient at fluctuation

• Additional resistance of the bulb depending on bulb

characteristics and its immersion.

),,,,,,( BTwpbM ACCCTBLfS =

wpC

FAPPAPP CkSVR )1(2

12

2 += ρ



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• Resistance of the appendages

– V = Ship speed

– = Wetted surface of the appendages

– = Form factor of the appendages

– = Friction resistance coefficient of the ship

FAPPAPP CkSVR )1(2

12

2+= ρ

APPS

21 k+

FC



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• Resistance of the immersed area of the transom and of

other parameters related to the immersed transom

• Correlation allowance for the model-ship extrapolation

– The correlation allowance depends on L and other

parameters

aA SCVR 2

2

1ρ=

TA



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Método Melhorado

• Differences to the standard method

– Form factor depending on the ship speed

– Revised formulas for the wave resistance

– Separate relations for the air resistance. In the standard

method it was included in the correlation allowance

• Other improvements:

– Added resistance due to incoming waves

– Added resistance from head wind

– Shallow water corrections


Improved method of Holtrop and Mennen

3. resistance of a ship - ulisboa · pdf file9 3. resistance of a ship 3.2 estimates based on...

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